SUPPLY CHAIN LOGISTICS NETWORKOPTIMIZATIONFOR … · stage supply chain network optimization problem. The objective of the research is to minimize the total cost of supply chain

International Journal on Mechanical Engineering and Robotics (IJMER)

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ISSN (Print): 2321-5747, Volume-2, Issue-1, 2014

12

SUPPLY CHAIN LOGISTICS NETWORKOPTIMIZATIONFOR

MINIMISING COST, CONSIDERING TRANSPORTATIONAL

DAMAGE

1Sojan Andrews Zachariah,

2Jeeno Mathew

1PG Scholar, Department of Mechanical Engineering, SJCET, Palai, 2Asst Prof., Department of Mechanical Engineering, SJCET, Palai,

Email : [email protected],

[email protected]

Abstract- In today’s vibrant and competitive environment,

companies are continuously trying to provide products and

services to end user at its best quality and satisfaction, and

also with better profit than the competitors do. Companies

realized that plenty of reasons prevail for a customer to

choose other competitors in the business. Managers have

learned that choosing partners and making alterations in

supply chain combinations have to be performed in the

supply chain level for being profitable and efficient in the

game and for making the customers delighted. Although

the resulting enterprise networks are more competitive, the

tasks for planning, management and optimization are

much more difficult and complex and to be decided with

least time. In this paper, we present a new method

developed using genetic algorithm for designing Multi

supplier and single warehouse chain where average cost of

a product over order filling is considered as the objective

for optimization. Product damage rate and product

damage cost are newly considered along with cost

components for assuring no defective product is delivered

to the end user. To show the result a numerical example is

taken from the literature.

Keywords – SCN Optimization, Genetic Algorithmand

Supply chain cost optimization.

I.INTRODUCTION

The business environment in the current world is

becoming increasingly uncertain, unpredictable,

complex, and as a result, highly competitive. Increased

competition makes companies to face the multi

challenges of reducing costs at the same time being

more responsive to the customers. The studies over these

issues throughout the world realized that, though there

may be diverse and situation specific solutions to the

problems posed by these challenges, flexibility has to be

the essential feature of the procedures used to handle

these variations. Due to the increase in competition and

complexity, Supply Chain Management (SCM) has

emerged as ahighly important issue for private as well as

public enterprises. A supply chain links - design,

sourcing, manufacturing, and logistics activities along

the organizations. The chain links suppliers and

customers, beginning with the production of raw

material by a supplier followed by the consumption of a

final product by the consumer. In a supply chain, the

flow of goods between a supplier and customer passes

through several stages, and each stage may consist of

many facilities [10].

In recent years, the supply chain network (SCN) design

problem has been gaining importance and are under the

limelight of serious and critical studies due to increasing

competitiveness introduced by the market globalization

[17,24,25]. The network design problem is one of the

most comprehensive strategic decision problems that

need to be optimized for long-term efficient operation of

whole supply chain. It determines the number, location,

capacity and type of plants, warehouses, and distribution

centers to be used. It also establishes distribution

channels, and the amount of materials and items to

consume, produce, and ship from suppliers to customers.

Most of supply chain network design problems can be

reduced to capacitated facility location problem (CFLP)

which is known to be NP-complete ; therefore, most of

supply chain network design problems are NP-

hard[26,27]. In the present article, a new method, has

been proposed and shows the application of it in the

SCN optimization problem. The SCN problem is a very

complex problem and the decision making is also very

difficult for the managers. In this study, a single

objective, minimization of the total average cost per fill

demand is considered. In this paper cost components

consists of a new introduction called product damage

mailto:[email protected]

mailto:[email protected]


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cost. This cost helps in finding better and safe

transportation and also the amount of damage product

derived by the algorithm ensures that no single damaged

product will reach the end user.Thesimulation is done

using simple genetic algorithm. To show the efficiency

of the proposed algorithm, a bench mark problem from

the literature has been taken and it is also tested on the

few moderate size of the problem. The remainder of this

paper is described as following: Section 2 presents the

literature review of supply chain network optimization

and employment of genetic algorithm in it. Section 3

delineates the complexity of the problems along with the

mathematical model. The optimization procedurehas

been described in Section 4. Section 5 is having the

details of case study for validation and section 6

describes the Results obtained and its analysis followed

y, section7 having conclusion and future proposals.

II. LITERATURE REVIEW

A. Single Objective Optimizations

In traditional SCM, the focus of the integration of SCN

is usually on single objective such as minimum cost or

maximum profit.

In literature, there are different studies dealing with the

design problem of supply networks and these studies

have been surveyed by Erenguc et.al. [1], Pontrandolfo

and Okogbaa [2]. In traditional SCM, almost all

researchers concentrated on optimizing single objectives

either minimum cost or maximum profit [3, 5, & 6].

These approaches are involved in tackling the various

components of costs or the tradeoffs between those

components. Amiri [3] has presented a lagrangian

relaxation approach to minimize the total cost of two

stage supply chain. Costa et al. [4] have worked on three

stage supply chain network optimization problem. The

objective of the research is to minimize the total cost of

supply chain. Jayaraman and Pirkul [7], Jayaraman and

Ross [8], Yan, Yu, and Cheng [9], Gen and Syarif [11]

and Truong and Azadivar [12] had considered total cost

of supply chain as an objective function in their studies.

B. Multi Objective Optimizations

However, there are no design tasks that are single

objective problems. Recently, multi objective

optimization of SCNs has been considered by different

researchers in literature. The design/planning/scheduling

projects are usually involving trade-offs among different

incompatible goals. Sabri and Beamon [10] developed

an integrated multi-objective supply chain model for

strategic and operational supply chain planning under

uncertainties of product, delivery and demand. While

cost, fill rates, and flexibility were considered as

objectives, ɛ-constraint method had been used as a

solution methodology. Chen and Lee [14] developed a

multi- product, multi-stage, and multi-period scheduling

model for a multi-stage SCN with uncertain demands

and product prices. As objectives, fair profit distribution

among all participants, safe inventory levels and

maximum customer service levels, and robustness of

decision to uncertain demands had been considered, and

a two-phased fuzzy decision-making method was

proposed to solve the problem. Erol and Ferrell [15]

proposed a model that assigning suppliers to warehouses

and warehouses to customers. They used a multi-

objective optimization modeling framework for

minimizing cost and maximizing customer satisfaction.

Guillen et.al. [16] Formulated the SCN design problem

as a multi-objective stochastic mixed integer linear

programming model, which was solved by ɛ-constraint

method, and branch and bound techniques. Objectives

were SC profit over the time horizon and customer

satisfaction level. Shen et.al. [18] Proposed an integrated

stochastic supply chain design model that takes into

consideration the location, inventory and routing costs.

They considered a three-tiered supply chain system

consisting of one or more suppliers, distribution centers

and customers with uncertain demand that follows a

certain probability distribution. Inventory holding costs

and transportation costs were assumed to exhibit

economies of scale. Cardona-Valdes et al. [19] have

presented a study of multi-echelon supply chain network

designing problem and they have considered the

economical aspect with customer service level Franca et

al. [22] proposed a multi-objective stochastic

programming model that seeks to find the supply chain

configuration that maximizes the profit and minimizes

defective materials from suppliers.Huang et al. [23]

studied three types of uncertainties in a closed-loop

supply chain of the Chinese steel industry: uncertainty

of time delay in remanufacturing and return, of costs are

considered.

C. Optimizations Using Genetic Algorithms(GA)

During the last decade, there has been a growing interest

using genetic algorithms (GA) to solve a variety of

single and multi-objective problems in production and

operations management that are combinatorial and NP

hard. Chanand Chung [13] proposed a multi-objective

genetic optimization procedure for the order distribution

problem in a demand driven SCN. They considered

minimization of total cost of the system, total delivery

days and the equity of the capacity utilization ratio for

manufacturers as objectives. Fulya Altiparmak et.al.

[17] In the study, they proposed a new approach based

on GA for multi-objective optimization of SCNs which

is one of the NP hard problems. Three objectives were

considered: (1) minimization of total cost comprised of

fixed costs of plants and distribution centers (DCs),

inbound and outbound distribution costs, (2)

maximization of customer services that can be rendered

to customers in terms of acceptable delivery time

(coverage), and (3) maximization of capacity utilization

balance for DCs (i.e. equity on utilization ratios). The

proposed GA was designed to generate Pareto-optimal


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solutions considering two different weight approaches.

To investigate the effectiveness of the proposed GA, an

experimental study using actual data from a company,

which is a producer of plastic products in Turkey, was

carried out into two stages. While the effects of weight

approaches on the performance of proposed GA were

investigated in the first stage, the proposed GA and

multi-objective simulated annealing (MO_SA) were

compared according to quality of Pareto-optimal

solutions in the second stage. Chan et.al. [13] Developed

a hybrid approach based on Genetic Algorithm (GA)

and Analytic Hierarchical Process (AHP) for production

and distribution problems in multi factory supply chain

models. Guillen et al. [16] have worked on multi-

objective supply chain network designing problem. They

employed a branch and bound algorithm and the

objectives are profit of supply chain and customer

service. Whereas, Altiparmak et al. [17] have considered

total cost, customer service and capacity utilization to

design a supply chain network. Prakash and Deshmukh

[20] have also presented an approach to allocate the

warehouse to the customers. They have also taken as a

multi-criteria problem by considering transportation

time and transportation cost. A hierarchical combination

of mixed-integer programming and a genetic algorithm

has been proposed in Truong and Azadivar [12] to

determine simultaneously the values of quantitative as

well as policy variables. Altiparmak et al. [17] have also

applied the GA to solve such problem with three

objectives: minimization of total cost, maximization of

customer service, and maximization of capacity

utilization. Farhani and Elahipana [21] have also applied

GA for distribution network optimization. They

considered two objectives: minimization of costs and

minimization of the backorders. Gen et al., [11] have

proposed a GA based approach to cope with network

multiple objective problems. Lee et al. [16] have also

applied the GA for the optimization of reverse logistics

network problem. From the aforementioned literature

review, it has been seen that the researchers are

concerned about the customer satisfaction i.e. to fulfill

the demand within time and decrease the cost.

III.MATHEMATICAL MODEL

A. Problem Description

In supply chain network designing problem, logistic cost

form the major part of a supply chain's costs. Inventory

control and distribution planning, as fundamental

logistical processes, affect the total costs of the supply

chain to a great extent, but, on the other hand, have a

great effect on the customer‟s demand fill rate. Every

suppliershould deliver the right amount of goods, at the

right time, and to the right place. In the present work, we

are considering an ongoing business with a supplier and

we are trying to redesign the network with another

alternative source such that best of the objectives can be

attained.Here the business scenario under consideration

is multiple suppliers (local and abroad) with same

product but with different unit product prices and cost of

services. The product is reached to the retailers

(considered as customer) who are having a uniform

demand for the product. The customer gets the product

from a single warehouse of a sole distributer who

engages with the supplier for the product upon the

demand from the customer. Each supplier is considered

having different modes of transport for carrying the

product to warehouse in accordance with their location.

The logisticscost vary according to the mode selected

for transport. The inventory is controlled by the

warehouse.

In this study, to evaluate the total cost, seven different

costs have been taken into consideration. These costs are

the engagement cost, purchasing cost, transportation

cost, inventoryholding cost, ordering cost, product

damage cost and penalty cost due to unfilled demand of

the orders.Along with cost total demand fill rate is also

evaluated consideringthat no damaged product reaches

the customer. In this study, since the damage rate is

considered, no product out of quality will reach the

customer.

B. Assumptions for formulation

Demand satisfied from single warehouse (total

demand in a period is only considered).

Customer is impatient; they are not ready to get the

backlogs satisfied, so backlogs are considered as

lost demand.

Non identical suppliers with single or multiple

mode of transport with variable parameters.

Periodic review of inventory, order placed if stock

is below ROP for a quantity Q.

The ROP and Q are initially decided.

Supplier as well as individual links will not take

order below 10 % of the order quantity for taking

advantage of the economies of scale.

No single damaged product will reach the customer.

C. Mathematical Formulation

1) Notations

i - Supplier's index (1, 2, 3…..n)

j - Transportation link„s index (1, 2, 3….m)

k- Number of days

O i - Number of orders placed to i th Supplier

Lij - Percentage of Damage through jth link of ith

supplier

2) Parameters

C Eng - Total Engagement Cost

Customer/Retailer


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C Inv - Total Inventory Cost

C Pur - Total Purchasing Cost

C Ord - Total Ordering Cost

C Trans- Total Transportation Cost

C Dmg - Total Damage Cost

d - Mean of Daily demand quantity

D Total- Total demand of items

D lost-Total unsatisfied Demand

CPLC -Total Penalty Cost on lost demand

p - Penalty cost per item

Ec i- Engagement cost for i th supplier

Npur-Number of items purchased from i th supplier

UCi-Unit purchasing cost (determined by i th supplier

N k - Inventory of items per day

h - Holding cost per item per day

Noi - Number of orders placed to i th supplier

oci - Ordering cost per order for i th supplier

Tr ij-Number of transshipped products from jth mode of

transportation link of i th supplier

Tcij-Transportation cost per item from jth transportation

link of i thsupplier

Tdmgij- Number of product that may get damaged

when transshipped through jth transportation

link of ith supplier

OR sup i- Order placed to i th supplier

LB sup ij- lower bound limit of order placed to i th

supplier (minimum number of items

ordered represented as % of Q)

3) Objective

The objective is to minimize the total average cost per

fill demand keeping satisfaction at constrain. The

mathematical formulation for the objective function is

given below.

F1 = CEng + CInv + CPur + COrd + CTrans+ CDMG +CPLC

DTotal-DLost(Eq.1)

To calculate the first objective, the individual cost can

be calculated as follows:

CEng = eci ∗ zini , Ɐi

(Eq.2)

Cpur = Nprchi ∗ UCini , Ɐi (Eq.3)

CDMG = ni lij ∗ TRij ∗ Uci ∗ Xijj (Eq.4)

Cord = ni noi ∗ oc ∗ yoio , Ɐio (Eq.5)

CTrans= ni TRij ∗ tcij ∗ Xijj , Ɐij (Eq.6)

Cinv= Nk ∗ hk (Eq.7)

CPLC = D Lost * p (Eq.8)

4) Constraints

The calculation of the above objectives are subjected to

the following constrains

ORsupii ≥ Dtotal (Eq.9)

TR supij≥ LB supij , Ɐij (Eq.10)

LB supij ≥0.10 (Eq.11)

OR supi = TRij∗ Xij

j , Ɐij (Eq.12)

ni TRij∗ Xij

j ≥Dtotal (Eq.13)

Xij= (Eq.14)

y oi= (Eq.15)

zi =

(Eq.16)

k,o,p, Nk ,Lbsupi ≥0 (Eq.17)

(Dtotal– Dlost)/DTotal ≥0.8DTotal (Eq.18)

The objective function (Eq. (1)) is to minimize the

average of all the incurred cost. The sixth cost

component is the damage cost which is the newly

introduced cost which will be incurred for the entire

product which reaches the warehouse in damaged

condition. Eqs. (2) to (8) show the formulation of

different costs like engagement cost, purchasing cost,

ordering cost, transportation cost, and inventory cost.

The novelty of this mathematical model is to penalize on

each lost demand. The penalty cost has been stated in

mathematical form in Eq. (8). The constraints are given

in Eqs (9) to (18). Eq. (9) shows that the order placed to

the supplier should not be less than demand of the

customers whereas Eq. (10) illustrates that the order

placed to an individual supplier should not be less than a

minimum number of items or lower bound of the order.

The total number of transshipped items from all the

transportation links of a supplier should be equal to the

order placed to that supplier and it should be more than

total demand from the customers. These constraints have

been modeled mathematically in Eqs. (10) and (11).

Finally, constraints in Eqs. (14)–(16) enforce the binary

nature of the configuration decisions while Eq. (17)

1 if jth transportation link of ith

supplier is activated 0 otherwise

1 if o th order is placed to i th

supplier

0 otherwise

1 if i th supplier is engaged

0 otherwise


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imposes the non-negativity restriction of the decision

variables corresponding to transshipment, orders

etc.Eq.(18) conveys that the number of satisfied demand

that is demand fill rate should be greater than 90% .

IV. PROCEDURE FOR OPTIMIZATION

A.Chromosome Representation

Fig.1 Chromosome structure

1)Segment 1

This segment represents the different suppliers those are

involved in the business. The decision represented by

this segment is that which all suppliers are selected for a

particular best combination of the supply chainnetwork.

Here the suppliers selected will provide the product of

same specification but with different cost parameters.

2)Segment 2

This segment represents the different modes of

transportations available for each supplier .The number

of modes may depend on the locational characteristics of

the suppliers. Upon selection of supplier the respective

modes of those suppliers will be included in the

segment.

3)Segment3

Replenishment policy is represented in this segment

where a reorder point and an EOQ will be represented

which will control the inventory flow for a given

demand.

B. Supplier selection

First task in the optimization is the selection of genuine

suppliers among the available suppliers global as well as

local. Among these genuine suppliers considering all

different parameters served by a supplier must be

collectively analyzed and best combination among them

should be decided for the achievement of the objectives.

Each supplier will be given two binary values „0‟ and

„1‟ where „1‟ indicates the supplier is selected and „0‟ if

not. There will be a potential supplier considered who is

providing the supplier some advantages and would be

considered in each combination. Other suppliers will be

selected in random combinations by varying the quantity

of products ordered from them.

C. Transportation mode selection

In order to handle the speed of arrival of the product at

central warehouse different modes of logistics are

considered. Number of different modes available for

each supplier depends on the location of the supplier. Ifa

supplier is selected during the above step the different

modes of logistics for the respective supplier will be

made live.

D. Quantity Allocation

A value between 0-100 will be randomly selected into

the different live genes of the selected supplier such that

sum of the values should be exactly equal to 100.

Considering the economies of a scale each value in

different genes should be greater than 10.these values

selected decides the percentage of the EOQ placed that

should be delivered by each supplier through respective

logistic mode. If any logistic mode is having a value less

than 10, that percentage will be distributed to other

potential mode of the respective supplier.

E. Replenishment policy

Replenishment policy differs from business to business

considering various factors like market demand, lead

times, inventory holding cost etc.In this method, R and

Q method is used also weekly review system is

introduced. A reorder point (ROP) will be decided in

relation to the demand and lead times of the different

suppliers who are engaged in thebusiness. During the

weekly review if the stock is found below ROP an order

for quantity Q will be placed.

F. Inventory flow

Inventory flow will be started with a base stock. Each

day a quantity equal to product demand will be reduced

from the stock and simultaneously the holding cost will

also be recorded. Number of product placed to each

supplier will reach the warehouse accordingly with the

lead times and will be added to the stock of that

particular day. The damaged product will be reduced

from the stock that is to be delivered to the customer

such that no faulty product reaches the customer which

will reduce level of customer satisfaction.

G. Cost components and calculation

In this study, to evaluate the total cost, seven different

costs have been taken into consideration. These costs are

the engagement cost, purchasing cost, transportation

cost, inventory holding cost, ordering cost, damage cost

and penalty cost due to unfilled demand of the orders.

The cost provided from all the suppliers and the duties

according to their physical situations. Purchase cost or

the unit product cost will vary from supplier to supplier

according to their facility and location. Engagement cost

is introduced when a new supplier is selected,

representing the costs for contract negotiation and so

forth. Transportation cost is calculated for each product

and may vary according the mode selected. A fixed

ordering cost will be placed for all orders placed

irrespective of the supplier. Damage cost is that cost

incurred by the distributor for keeping the faulty product

with him and not delivering it to the customer. Penalty

cost is the cost that will be added to the total supply

chain cost in case of failure to meet customer demand.


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Start

Randomly select new suppliers

Maintaining the potentialsupplier

Making the modes of selected suppliers

live

Allocating „%‟, indicating amount of products carried by each link of the selected suppliers

Checking „%‟allocated to each link are >10% of Q

If

Distribute the %‟s <10 to the next potential mode

Run the inventory flow for the simulation period

Calculate the Number of orders placed, Backorders created, Total demand

Calculate the cost and demand fill rate for the particular combination for the simulation period

Apply GA

Optimal solution

Stop

No

H. Demand fill- rate calculation

Demand fill rate indicates how much percentage of the

total demand from market is satisfied. This gives a

measure of customer satisfaction. It is calculated by

knowing the total demand came for the entire period and

the number of backorders created for the period. The

demand fill-rate is kept in constrain.

I .Simple Genetic algorithm operations (SGA)

Steps involved in SGA are:

Fig.2 Optimization flowchart

1) Population Initialization

A population is a collection of individuals. A population

consists of a number of individuals being tested, the

phenotype parameters defining the individuals and some

information about search space. The two important

aspects of population used in Genetic Algorithms are:

The initial population generation.

The population size.

For each and every problem, the population size will

depend on the complexity of the problem. It is often a

random initialization of population is carried. In this

case a binary coded chromosome (segment 1) is

initialized to a random zero or one. For each random

selection the integer values at segment two also varies

randomly from 0-100. And the values at the 3rd

segment

are constant which is calculated initially. Here the

initialization of population is carried out without any

known good solutions. The first population have a gene

pool size is varied in order to be able to explore the

whole search space.

All the different possible alleles of each gene are present

in the population. To achieve this, the initial population

is, in most of the cases, chosen randomly. The size of

the population was raised for fewcases. The larger the

population is, the easier it is to explore the search space.

But it has established that the time required by a GA to

converge is O (nlogn) function evaluations where n is

the population size. We say that the population has

converged when all the individuals are very much alike

and further improvement may only be possibly by

mutation. Practically, a population size of around 100

individuals is found to be quite frequent, but anyway

this size can be changed according to the time and the

memory disposed on the machine compared to the

quality of the result to be reach

TABLE 1: INITIAL POPULATION

Segment 1

Random

generated

Population

Size(n)

Chromosome 1 1 1 1 0

Chromosome 2 1 0 1 0

. .

. .

. .

Chromosome n 1 1 11

2)Selection

Selection is the process of choosing two parents from

the population for crossing. After deciding on an

encoding, the next step is to decide how to perform

selection i.e., how to choose individuals in the

population that will create offspring for the next

generation and how many offspring each will create.

The purpose of selection is to emphasize fitter

individuals in the population in hopes that their off


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springs have higher fitness. Chromosomes are selected

from the initial population to be parents for

reproduction. The problem is how to select these

chromosomes. According to Darwin‟s theory of

evolution the best ones survive to create new offspring.

Selection is a method that randomly picks chromosomes

out of the population according to their evaluation

function. The higher the fitness function, the more

chance an individual has to be selected. The selection

pressure is defined as the degree to which the better

individuals are favored. The higher the selection

pressured, the more the better individuals are favored.

This selection pressure drives the GA to improve the

population fitness over the successive generations.

Selection has to be balanced with variation form

crossover and mutation. Too strong selection means sub

optimal highly fit individuals will take over the

population, reducing the diversity needed for change and

progress; too weak selection will result in too slow

evolution. There are different selection methods, for this

work roulette wheel selection is used.

Roulette selection is one of the traditional GA selection

techniques. The commonly used reproduction operator is

the proportionate reproductive operator where a string is

selected from the mating pool with a probability

proportional to the fitnessupon a fitness function and the

fitness function used in this study is[29]:

Fitness = (Eq 19

Where f(x) is the individual function F1 calculated along

eachchromo some.

The principle of roulette selection is a linear search

through a roulette wheel with theslots in the wheel

weighted in proportion to the individual‟s fitness values.

A target value is set, which is a random proportion of

the sum of the fitness‟s in the population. The

population is stepped through until the target value is

reached. This is only a moderately strong selection

technique, since fit individuals are not guaranteed to be

selected for, but somewhat have a greater chance.

A fit individual will contribute more to the target value,

but if it does not exceed it, the next chromosome in line

has a chance, and it may be weak. It is essential that the

population not be sorted by fitness, since this would

dramatically bias the selection. The above described

Roulette process can also be explained as follows: The

expected value of an individual is that fitness divided by

the actual fitness of the population. Each individual is

assigned a slice of the roulette wheel, the size of the

slice being proportional to the individual‟s fitness. The

wheel is spun N times, where N is the number of

individuals in the population. On each spin, the

individual under the wheel‟s marker is selected to be in

the pool of parents for the next generation.

This method is implemented as follows:

a). Sum the total expected value of the individuals in the

population. Let it be T.

b). Repeat N times:

i. Choose a random integer „r‟ between o and T.

ii. Loop through the individuals in the population,

summing the expected values, until the sum is greater

than or equal to „r‟. The individual whose expected

valueputs the sum over this limit is the one selected.

Roulette wheel selection is easier to implement but is

noisy. The rate of evolutiondepends on the variance of

fitness‟s in the population.

3)Crossover

The traditional genetic algorithm uses single point

crossover, where the two mating chromosomes are cut

once at corresponding points and the sections after the

cuts exchanged. Here, a cross-site or crossover point is

selected randomly along the length of the mated strings

and bits next to the cross-sites are exchanged. If

appropriate site is chosen, better children can be

obtained by combining good parents else it severely

hampers string quality.

Single point cross over is done at the second segment in

a stage when the allele values are binary in nature. The

cross over site selection is random based on the length

of the string. As the cross over takes place the program

checks whether the supplier is made live or not,

otherwise those chromosomes will be discarded as a

filtration process for reducing the simulation

complexity.

TABLE 2: CROSSOVER REPRESENTATION

Segment 2

Parent

Chromosome

Chromosome

1 1 1 1 1 1 1

1

0

Chromosome

2 1 0 1 0 1 1

0

1

Child

Chromosome

Offspring 1 1 1 1 1 1 1

0

1

Offspring2 1 0 1 0 1 1

1

0

4)Mutation

After crossover, the strings are subjected to mutation.

Mutation prevents the algorithm to be trapped in a local

minimum. Mutation plays the role of recovering the lost

genetic materials as well as for randomly disturbing

1

1+f (xi)


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19

genetic information. It is an insurance policy against the

irreversible loss of genetic material. Mutation has

traditionally considered as a simple search operator. If

crossover is supposed to exploit the current solution to

find better ones, mutation is supposed to help for the

exploration of the whole search space. Mutation is

viewed as a background operator to maintain genetic

diversity in the population. It introduces new genetic

structures in the population by randomly modifying

some of its building blocks. Mutation helps escape from

local minima‟s trap and maintains diversity in the

population. It also keeps the gene pool well stocked, and

thus ensuring ergodicity. A search space is said to be

ergodic if there is a non-zero probability of generating

any solution from any population state. There are many

different forms of mutation for the different kinds of

representation. For binary representation, a simple

mutation can consist in inverting the value of each gene

with a small probability. The probability is taken about

1/L, where L is the length of the chromosome. Mutation

of a bit involves flipping a bit, changing 0 to 1 and vice-

versa for the same segment of string where crossover

has been conducted.

5) Selection of the best solution

After the mutation since the function is minimization,

the minimum of the set is stored. At each subsequent

generation this best will be replaced if another value less

than the pre stored value comes .since the demand fill

rate is kept as constrain the selection of value checks the

region where the demand fill rate is and if it is a

permissible valuethe lowest average cost gets in, else

will be discarded.

When the termination criteria is reached the optimal best

solution will be displayed which will give an idea how

the SCM network should be designed for a specific

inventory policy.

TABLE 3: MUTATION OPERATION

REPRESENTATION

Segment 2

Before

Mutation

Offspring 1 1 1 1 1 1 1 0 1

Offspring 2 1 0 1 0 1 1 1 0

After

Mutation

Mutated

Offspring 1

1 1 1 1 0 1 0 1

Mutated

Offspring2

0 0 1 0 1 1 0 0

V.VALIDATION

A. Industrial Profile in Case Study

The proposed case study is part of the supply chain for

„„Classic‟‟ boots of an Italian textile company [11]. The

company outsourced production to outside contractors

and it focuses only on marketing issues. For the actual

situation (Fig. 3), the product is made by a unique

supplier in Vietnam (Supplier 1or S1). Boots are then

collected in containers and transported by boat from

Hochimin harbor to Genova harbor. From Genoa, boots

are transported by trucks to the central warehouse near

Ferrara, where they are stored. The product is then

distributed to the retailers of the Italian market. The

overall objective is to redesign the supply chain, mainly

by: Evaluating different configurations by selecting new

suppliers plus transportation links, basing the choice

upon criteria as global cost and customer service level,

Evaluating the sensitivity of the solutions to the market

demand variation, Evaluating the impact of data

uncertainty on the reliability ofthe supply chain and

Evaluating the effects of changes in the central

warehouse inventory policy.

Fig.3: SCM for the case study

The suppliers to considerare: Actual supplier (Supplier

1-S1), a new supplier in Far East (Supplier 2-S2), a new

supplier in East Europe (Supplier 3-S3) and a new

supplier in Italy (Supplier 4-S4). More specifically, one

potential supplier, denoted by Supplier 1-S1, who is

already in the business and a portion of the total

quantity, should be mandatorily given to S1. In order to

reduce the order-to-delivery lead-time, the company

proposes additional transportation.In this study, to

evaluate the total cost, seven different costs have been

taken into consideration. These costs are the engagement

cost, purchasing cost, transportation cost, inventory

holding cost, ordering cost, Damage cost and penalty

cost due to unfilled demand of the orders. The cost

provided from all the suppliers and duties according to

their physical situations are given in Table 4. From the

table, it is clearly shown that supplier 2 provides the

boots at the lowest cost. Likewise features of each

supplier vary among each. The transportation features

are provided in Table 5.The main objective to solve such

supply chain network optimization problem is to

evaluate the selection of different suppliers or set of the

suppliers and transportation links simultaneously,

whereas the performance criteria are the total cost and


__________________________________________________________________________


20

demand fill rate. Simultaneously, this study also satisfies

some other goals like the impact of the performance by

demand variation and the impact of inventory policy

changing. From the figure, supplier 1 is the actual or

existing supplier which is situated in Vietnam and one of

the new or proposed suppliers (supplier 2) is in the Far

East whereas supplier 3 is in the East Europe and the last

one (supplier 4) is the local supplier i.e. that is situated

in Italy itself. Supplier has a daily demand of 300 with a

variance of 50

B. Supplier parameters

Different suppliers poses different feature depending

upon the location, manufacturing methods, manpower

availability, resource availability, taxes and duties

,different government policies etc. by selecting different

suppliers we can extract the best from each suppliers,

and also get the products with different prices according

to the demanded situations. There will be some potential

supplier present in supply chains who can provide

products with competitive prices. Main components

considered while observing suppliers are engagement

cost, purchase cost ordering cost and lead-times. Details

are given in Table: 4

TABLE 4: SUPPLIER PARAMETER DETAILS

Suppli

er ID

Engage

ment

cost

Price

per

pair

Duties

Suppl

y

lead-

time

(day)

Lea

d

Tim

e

Min.

order

size

(pair)

1 0 12£ 10% 15 0.10*Q

2 100000£ 10£ 20% 20 0.10*Q

3 80000£ 14£ 0 10 0.10*Q

4 100000£ 16£ 0 8 0.10*Q

C. Transportation parameters

As mentioned in the topic selection of supplier,

transportation attributes are also depended on various

external as well as internal factors. Major factors that

have got remarkable effect on transportation parameter

are locational terrain, availability of transportation

modes, technological development of the area of

suppliers, Location of warehouse, nature of demand.

Etc. main components considered here for fixing

transportation cost are the unit logistic cost, damage rate

through each mode and the lead-times caused by

different modes. For this study modes of transport

available for S1 areL11, L12 and L13 whereas L21,

L22, L23 represents modes for S2 and L3, L4 for S3 and

S4 respectively. Details are given in table: 5

D. Inventory Replenishment policy

Product replenishment in this a case follows R and Q

approach where a demand is there on that basis a

Reorder level is calculated .For this study R is kept as

6351and Q as 1652.Upon reaching the ROP level an

order quantity is placed. At each order placed an order

cost will be incurred. Based on the daily demand the

warehouse inventory varies and the number of received

product demand and number of lost demands due to

damage as well as lack of responsiveness is analyzed.

Components for optimization calculated are the penalty

cost and the average inventory holding cost for Product

details are given in table: 6

TABLE 5: TRANSPORTATION PARAMETER

DETAILS

ID

Lead

Time(Days)

Unit

Logistics

cost Per pair

Damage Rate

L11 20 0.5£ 0.02

L12 8 2£ 0.05

L13 5 4£ 0.01

L21 25 0.5£ 0.02

L22 10 2£ 0.05

L23 5 4£ 0.01

L3 4 1£ 0.01

L4 2 0.2£ 0.01

TABLE 6: INVENTORY COST PARAMETERS

Ordering

cost/unit 100£

Penalty

cost/unit 2£

Inventory

cost/unit 2.5£

VI.RESULT ANALYSIS

A. Results Obtained

The final result analysis conveys many advantages of

the algorithm method for optimization

We ran the optimizer for different generations and

population sizes. The possibilities of crossover and

mutation are set as 0.9 and 0.3, respectively. Roulette

wheel selection and random one-point crossover are

employed. Considering supply chain cost as average

cost in this caseis critical for the company, focus is on

the analysis of solutions that keep the average cost at its

best. Below given Tables7-9 shows the different

solutions obtained at different GA parameters. It

exhibits the distribution of the best-so-far optimal

solutions with a demand fill-rate higher than 90%. We


__________________________________________________________________________


21

summarize several important solutions from these tables.

We note that the solutions in the best-so-far solutions set

are composed of basically two categories of supply

chain network structures.

TABLE7: SCM STRUCTURE FOR POP SIZE 10 &

1000GENERATION

S1

L1

1

S

1

L

12

S

1

L

13

S

2

L

21

S

2

L

22

S

2

L

23

S

3

L

3

S

4

L

4

ROP Q SP F1

70 16 14 0 0 0 0 0 6351 1652 365 20.

2


1000GENERATION

S1

L1

1

S

1

L

12

S

1

L

13

S

2

L

21

S

2

L

22

S

2

L

23

S

3

L

3

S

4

L

4

ROP Q SP F1

56 17 15 0 0 12 0 0 6351 1652 36

5 19.56


500GENERATION S

1

L

11

S

1

L

12

S

1

L

13

S

2

L

21

S

2

L

22

S

2

L

23

S

3

L

3

S

4

L

4

ROP Q SP F1

43 35 11 0 0 11 0 0 6351 1652 36

5 19.29

B. Result Analysis

We run the optimizer for different generations as 1000

and 500 respectively with a population size of at 10 and

100 respectively. The possibilities of crossover and

mutation are set as 0.9 and 0.1, respectively. Roulette

wheel selection and random one-point crossover are

employed. Each of the points represented on the specific

solution. In the results obtained integers (example in

Table 8): values 56 and 17 under S1L11 and S1L12

respectively indicate that 56 % and 17 % of the total

ordered quantity will be supplied through the respective

modes. According to the Table 8 the SCN will comprise

of supplier 1 and supplier 2, at the same time first and

second transportation modes of supplier 2 will not be

employed.

We summarize several important solutions in above

given tables, we note that the solutions in the best-so-far

set are composed of basically two categories of supply

chain network structures. SuppliersS1 and S2 are

advisable also the L22 mode of the supplier two is not

utilized. The cost obtained will be approximately 19 £.

The penalty cost is assumed to be 2.5£ per piece. Also

result shows for a demand fill rate above 90 percent also

at more a time employs the suppliers S1 and S2 since

they can supply at better performance.

The variation pattern in the result is obtained due to the

introduction of penalty cost as well as the newly

introduced damage cost i.e. If better transportation is

used although their cost is bit high it can be effectively

saved by avoiding the penalty cost and damage cost.

The proposed heuristic method has been coded in

MATLAB. While we look about the algorithm the

results obtained at different convergence i.e. the results

obtained at 1000, 500and with population sizes of 10

and100 are exhibiting almost same solutions. It is

mainly due to the way of iterations conducted. At each

genetic operation the percentage allocation of product

supplied by each supplier also gets iterated inside the

program simultaneously. This enables the algorithm to

search for more result at lesser generations which can

save the time of simulation.

VII.CONCLUSION

An overview of a simulation based assessment and

optimization of enterprise networks has been provided.

In addition, the method was applied to a real life case

study proposed by a textile industry. It was shown, that

the method can be helpful for finding solutions for big

business enterprises that have to get into the market at

lesser time. Because the dynamic of a system

comprising a huge number of more or less independent

acting self-controlled entities within a network is hardly

to predict and evaluate in real operation, appropriate

tools are required for this purpose. Beside an assessment

of the overall network, other aspects related to

individual facilities or entities like specific control

strategies could be tested and improved by using such a

method. Due to its open and flexible architecture, this

algorithm seems to be a perfect base for an

adaptation/enhancement necessary in order to support

such scenarios as well. Some benchmarking works are

also to be done for approach performance assessment,

comparing to the results obtained by analytical methods.

The present work provides a new insight to the

practitioner to solve the different combinatorial

problems e.g. network optimization in the supply chain

context. The network optimization in the flexible supply

chain context is a very complex problem for the

practitioners.

The algorithm mainly emphasizes on the initialization,

selection and genetic operators.

This research has enlightened the domain of supply

chain network optimization as it discusses about the

commitment of faster delivery at minimum cost. The

mangers can apply the solutions with providing more

constraints accordance with the environment of the

market and supply chain. The network optimization

problem can also give a new vision to the managers of

supply chain to achieve the solution in such a way that

can fulfill the demand of the customer with minimum

average cost per product. Therefore, it will provide a

two dimensional approach at the same time. This

research provides a new insight about the optimization


__________________________________________________________________________


22

algorithms in theoretical manner but it can be employed

in real industry problems also with some new constraints

and the numerical analysis proved the same concept. As

a future work, this research can be stretched out to

various problems of the supply chain environment that

having multi- product scenarios. This research can also

be employed for JIT or flexible manufacturing situations

where multi objectives goal are present.

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SUPPLY CHAIN LOGISTICS NETWORKOPTIMIZATIONFOR … · stage supply chain network optimization problem. The objective of the research is to minimize the total cost of supply chain